A Promising High-Entropy Thermal Barrier Material with the Formula (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12

YSZ has been widely used as a TBC material, but its phase change at high temperatures limits its development, thus the need for developing new thermal barrier materials resistant to high temperatures. Rare-earth aluminate ceramics with a garnet structure (Yb3Al5O12) have been considered as a potential thermal barrier material. The melting point of Yb3Al5O12 is 2000 °C, which has a potential high temperature application prospect. However, Yb3Al5O12 has lower thermal expansion and higher thermal conductivity than YSZ, which is a widely employed thermal barrier coating (TBC) material. To overcome these obstacles, (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12, a high-entropy ceramic, was prepared by a solid-state reaction and pressureless sintering. The thermal conductivity of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 was 3.48 W/(m·K) at 300 K, approximately 25.48% lower than that of the Yb3Al5O12 (4.67 W/(m·K)). The thermal expansion coefficient of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 was 9.28 × 10−6 K−1 at 673-1273 K, approximately 18.52% higher than that of the Yb3Al5O12 (7.83 × 10−6 K−1, 673-1273 K). When the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 was annealed at 1550 °C for 7 days, its average grain size only increased from 0.7 μm to 1.3 μm. Moreover, the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 exhibited better chemical stability and a lower grain growth rate than the Yb3Al5O12. This study reveals that (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 is a promising candidate for the future generation of thermal barrier materials.


Introduction
Thermal barrier coatings (TBCs) are widely employed in gas turbine engines for aerospace, power generation, and marine applications and can protect the superalloy by reducing the alloy surface temperature and increasing the engine efficiency of gas turbines [1][2][3][4][5][6]. TBCs must be able to withstand extreme temperature cycling and thermal shock [7][8][9]. Therefore, the selection of TBCs is restricted by some basic requirements: (1) excellent high-temperature stability, (2) a thermal expansion coefficient (TEC) consistent with the metallic substrate, (3) a low grain growth rate, (4) low thermal conductivity, and (5) chemical inertness. To date, YSZ has been widely employed as a TBC material, but the limitations of phase transformation at a high temperature and high oxygen diffusivity make it unsuitable for the high operating temperature of gas turbine engines [10,11]. At high temperatures, the non-equilibrium tetragonal phase in YSZ is prone to decomposition to generate t-phase and c-phase, and the cumulative effect of the volume expansion due to the phase change will cause cracks in the coating. Moreover, oxygen ions from YSZ above 800 • C tend to oxidize the metal substrate through the coating [12][13][14]. Therefore, YSZ cannot serve for a long time at temperatures above 1200 • C. Thus, novel TBC materials with better high-temperature stability are urgently needed.
The physicochemical properties of rare-earth elements have made them a research priority in the field of thermal barrier coatings [15][16][17]. Wang et al. reported that the thermal barrier coating of La 1.4 Nd 0.6 Zr 2 O 7 (LNZ) on a Mo substrate was prepared by air plasma spraying with a self-developed LNZ thermal spray powder [18]. Xu et al. reported that (Sm 0.2 La 0.8 ) 2 (Zr 0.7 Ce 0.3 ) 2 O 7 (SmLZC), as a candidate material for novel thermal barrier coatings, was prepared by electron beam-physical vapor deposition (EB-PVD) [19]. Thus, rare-earth oxides exhibit good feasibility in the field of thermal barrier coatings. Therein, Yb 3 Al 5 O 12 exhibits excellent high-temperature stability, isotropic elastic properties, and low intrinsic thermal conductivity and has recently been recognized as a potential thermal barrier material [20][21][22][23]. The melting point of Yb 3 Al 5 O 12 is 2000 • C, which has a potential high-temperature application prospect. Moreover, theoretical results obtained by Klemm confirmed that Yb 3 Al 5 O 12 has better chemical stability than several other promising TBCs, such as Y 2 Si 2 O 7 and Yb 2 Si 2 O 7 [24]. However, Yb 3 Al 5 O 12 has lower expansion and higher thermal conductivity than YSZ, which is a widely used TBC material [22]. The linear thermal expansion of Yb 3 Al 5 O 12 was in the range from 298 to 1273 K, 7.83 × 10 −6 K −1 , which was lower than that of YSZ ((10-11) × 10 −6 K −1 ). The measured thermal conductivities of Yb 3 Al 5 O 12 at 300 and 1400 K are 4.67 W/(m·K) and 2.05 W/(m·K), which were greater than those of YSZ. Thus, decreasing the thermal conductivity of Yb 3 Al 5 O 12 and increasing the coefficient of thermal expansion of Yb 3 Al 5 O 12 are critical to expanding its applications.
Currently, the emergence of high-entropy ceramics (HECs) has attracted attention [25][26][27][28][29][30]. It has been reported that HECs efficiently enhance the thermal performance of thermal barrier materials because they have higher temperature stability, more consistent TECs, and a slower grain growth rate than single-component compounds. Lattice distortion and component disorder can increase phonon scattering and thus reduce thermal conductivity. In addition, better chemical stability can be achieved due to retarded diffusion. Some researchers have successfully synthesized different kinds of high-entropy oxides (HEOs) for TBC applications. An increase of 6 h in annealing results in only a 1 µm increase in grain size for (5RE 0.2 )Ta 3 O 9 , while this increases to approximately 3 µm for EuTa 3 [34]. Thus, HECs can effectively enhance the combined properties of thermal barrier materials.
Herein, we design and synthesize a promising high-entropy rare-earth aluminate ceramic with garnet, (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 , by the solid-state reaction method. The standards for the component design are as follows: (1) to guarantee the formation of solid solutions, differences in the size of the rare-earth ions must not be greater than 15.0%; (2) each component must have the structure of garnet; and (3) no phase change may occur at the working temperature. In addition, in terms of the selected elements, we try to use lowcost rare-earth elements to further reduce the economic problem. The thermal expansion coefficient, thermal conductivity, high-temperature stability, chemical inertness and hardness of (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 are studied in the present work. These properties are valuable and beneficial to the potential application of (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 as the future generation of thermal barrier materials.  Figure 1 shows the synthesis of (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 via a solid-state reaction. The total molar ratio of rare-earth elements to Al was 3:5. First, five rare-earth oxides with equal molar ratios were mixed with Al 2 O 3 and alcohol, and ground at 360 r/min for 10 h using a planetary ball mill. Afterward, the obtained solution was dried in an oven at 80 • C for 10 h. The obtained powder mixture was pressed and molded at 5 MPa. Afterwards, the (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 powders were synthesized by sintering at 1600 • C for 2 h. The as-prepared powder was ball-milled for 10 h and then dried and sieved through a 400 mesh sieve to obtain fine particles. The samples were densified by the pressureless sintering method. The process of cold isostatic pressing is that the powder is pressed through a mold, then pressed again in a cold isostatic press at a pressure of 200 MPa to make itself more dense, and then calcined in a muffle furnace at a temperature of 1650 • C for 5 h. Finally, the densified bulk samples can be obtained.

Experimental Section
hardness of (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 are studied in the present work. Al2O3 (99.999%) were purchased from Aladdin Reagent Ltd., Co. (Shanghai, Ch ure 1 shows the synthesis of (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 via a solid-state reac total molar ratio of rare-earth elements to Al was 3:5. First, five rare-earth oxi equal molar ratios were mixed with Al2O3 and alcohol, and ground at 360 r/min using a planetary ball mill. Afterward, the obtained solution was dried in an ov °C for 10 h. The obtained powder mixture was pressed and molded at 5 MPa. Aft the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 powders were synthesized by sintering at 1600 h. The as-prepared powder was ball-milled for 10 h and then dried and sieved th 400 mesh sieve to obtain fine particles. The samples were densified by the pre sintering method. The process of cold isostatic pressing is that the powder is through a mold, then pressed again in a cold isostatic press at a pressure of 200 make itself more dense, and then calcined in a muffle furnace at a temperature o for 5 h. Finally, the densified bulk samples can be obtained.

Characterization of the Materials
A scanning speed of 2°/min was used for X-ray diffraction (XRD, Miniflex 60 ment, Tokyo, Japan) with Cu Kα radiation to determine the phase structure of the samples. Scanning electron microscopy (SEM, Apreo S LoVac Thermo Fisher S Waltham, MA, USA) was combined with field-emission transmission electron mi (TEM, FEI/Talos F200X G2, Lincoln, NE, USA) and energy-dispersive spectromet to examine the morphology and chemical composition of the samples. The

Characterization of the Materials
A scanning speed of 2 • /min was used for X-ray diffraction (XRD, Miniflex 600 instrument, Tokyo, Japan) with Cu Kα radiation to determine the phase structure of the powder samples. Scanning electron microscopy (SEM, Apreo S LoVac Thermo Fisher Scientific, Waltham, MA, USA) was combined with field-emission transmission electron microscopy (TEM, FEI/Talos F200X G2, Lincoln, NE, USA) and energy-dispersive spectrometry (EDS) to examine the morphology and chemical composition of the samples. The TEC of the bulk samples was determined by a thermal expansion meter (Cryoall C15V, Beijing, China) with a size of Φ 30.0 mm × 2.0 mm. The thermal conductivity of the bulk samples was examined by a thermal constant analyzer (TPS 2500, Hot Disk, Göteborg, Sweden) with a size of Φ 6.0 mm × 10.0 mm. The thermal conductivities of the dense materials were corrected by the following Formula (1) [35].
where K S is the thermal conductivity obtained by the test, K is the thermal conductivity of the fully dense materials, and P is the porosity. A Vickers hardness test was conducted using a micro hardness tester (FT FM-700, Tokyo, Japan). The samples for Vickers hardness testing were cut by a diamond saw from the as-prepared bulk material and then polished down to 1.0-µm diamond grits. The Vickers hardness number was determined by a microhardness tester with loads of 1, 3, 5, Materials 2022, 15, 8079 4 of 12 and 10 N, respectively. Loads of 1, 3, 5, and 10 N were applied with a dwell time of 15 s. The Vickers hardness tests were calculated by using Formula (2).
where P is the load, and d is the diagonal length of indentation. Five measurements for each load were taken to obtain the average value of hardness. The cell dimension was calculated by the Rietveld refinement using GSAS software (EXPGUI-GSAS), and the reliability factors of R p and R wp were calculated by using Formulas (3) and (4) [36].
The Archimedes method was used to measure the bulk density (ρ), while Formula (5) was used to calculate the theoretical density.
where m is the mass of a unit cell of HE-RE 3 Al 5 O 12 and V is the cell volume. The relative density was calculated from the ratio of the actual density to the theoretical density (ρ/ρ th ).
The concentrations of dissolved ions in the leachates were determined by inductivitycoupled plasma mass spectrometry (ULTIMA 2, Horiba Jobin Yvon S.A.S, Edison Township, NJ, USA). A leaching test of the bulk samples by atmospheric pressure sintering at 1640 • C for 5 h was performed in a nitric acid solution in PTFE for 1-5 d. The HE-RE 3 Al 5 O 12 ceramics, which had a diameter of 15 mm and a height of 2 mm, were polished, cleaned, and dried. The ratio of the geometric surface area of the sample to the volume of the leachate was maintained at 1:10 cm −1 . The normalized element mass leaching rates (LR i ) of the (Al) were obtained based on Formula (6) [37].
where C i is the concentration of elements (Al) in the leaching solution, V is the volume of the leaching solution, f i is the proportion of element I in the ceramic, S is the surface area of the ceramic, and t is the date of leaching.  Figure 3a shows the XRD patterns of the calcined powder and the sintered solid. The XRD patterns were consistent before and after calcination, indicating that no impurities were introduced. The absence of holes and cracking can be seen in the SEM image in Figure 3b, indicating that the sintered (Y 0. 2     As shown in Figure 4, the cell dimension of the (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 was calculated by the Rietveld refinement using GSAS software, and the reliable factors calculated via the equations are R p = 3.38% and R wp = 4.41%. The refinement results are generally considered reliable for values of R p and R wp below 10.00%. The (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 ceramic lattice parameters were found to be a = b = c = 11.992 Å, which is approximately equal to the average cell size of the five single components (11.986 Å). Table 1 shows the refined cell dimensions and theoretical density of (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 and the five single-component garnets obtained from jade. The theoretical density of (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 was 6.02 g/cm 3 , based on the refined cell parameters. The sintered density, calculated by Archimedes' approach, is 5.88 g/cm 3 , 97.67% of the theoretical value (6.02 g/cm 3 ).   Figure 5 shows the high-angle annular dark-field (HAADF) image and element mapping of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 powders. The distribution of elements is clearly uniform, demonstrating the uniformity of the solid solution. The XRD and TEM-EDS results suggest that single-phase aluminates with excellent chemical uniformity were synthesized by the solid-state reaction approach. Figure 6a shows that the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 ceramics were further characterized by HR-TEM. Two positions were selected to calculate the lattice fringes, which exhibited typical (211) and (420) lattice planes with D-spacings of 0.488 nm and 0.267 nm, respectively. These results are consistent with the broad XRD peaks of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 at 18.2° (0.48665 nm, (211)) and 33.5° (0.26662 nm, (420)). The selected area electron diffraction (SAED) pattern of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 powders (Figure 6b) shows that (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 has a single-crystal ordered garnet structure.   Thermal conductivity is essential for assessing the thermal insulation properties of insulating materials. Table 2 shows the thermal conductivity of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12, (Y0.2Yb0.2Lu0.2Eu0.2Er0.2)3Al5O12, and Y3Al5O12 at 300 K. The thermal conductivity of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 ceramics was found to be 3.48 W/(m·K) at 300 K, approximately 25.48% and 8.66% lower than that of Yb3Al5O12 (4.67 W/(m·K)) and (Y0.2Yb0.2Lu0.2Eu0.2Er0.2)3Al5O12 (3.81 W/(m·K)), indicating that (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 is a potential thermal barrier material [32]. The thermal conductivities of rare-earth aluminates are slightly higher than commercial TBC material YSZ, which is 2.50-3.20 W/(m·K) [38]. Five equimolar rare-earth cations are present in (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 at crystallographic sites randomly occupying the same lattice. The mismatch between the masses and radii of these cations leads to large lattice distortions and intense phonon scattering in the material. Among the four core effects of high-entropy materials is lattice distortion, which may play a significant role in the decrease in the thermal conductivity of garnets [39].  Thermal barrier materials need to possess a coefficient of thermal expansion similar to that of a high-temperature alloy matrix because a thermal expansion mismatch can cause cracking of the matrix. Figure 7 shows the curves of the linear thermal expansion of (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12, determined from room temperature to 1273 K. The relative changes in the length of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 samples were recorded with the increasing temperature.
A low grain growth rate is very important for TBC materials, as it improves the crack resistance due to thermal stress and prevents an increase in thermal conductivity. Figure  8 shows the average grain sizes of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 ceramic specimens after annealing at 1550 °C for 7 days. As seen in Figure 8, the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 ceramics have a lower average grain rate than the Yb3Al5O12 and Er3Al5O12. The grain growth rates of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12, Yb3Al5O12, and Er3Al5O12 samples were similar during the annealing period of 0-5 days at 1550 °C. However, when the annealing time was extended to 7 days, the grain growth rate of the high-entropy aluminate was less than that of the Yb3Al5O12 and Er3Al5O12 under the same conditions. As a result of sluggish Thermal conductivity is essential for assessing the thermal insulation properties of insulating materials. Table 2 [32]. The thermal conductivities of rare-earth aluminates are slightly higher than commercial TBC material YSZ, which is 2.50-3.20 W/(m·K) [38]. Five equimolar rare-earth cations are present in (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 at crystallographic sites randomly occupying the same lattice. The mismatch between the masses and radii of these cations leads to large lattice distortions and intense phonon scattering in the material. Among the four core effects of high-entropy materials is lattice distortion, which may play a significant role in the decrease in the thermal conductivity of garnets [39]. Thermal barrier materials need to possess a coefficient of thermal expansion similar to that of a high-temperature alloy matrix because a thermal expansion mismatch can cause cracking of the matrix. Figure 7 shows the curves of the linear thermal expansion of (Y 0.  Thermal barrier materials must have excellent chemical inertness. Figure 9 shows the normalized elemental leaching rates of Al in (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 and Yb3Al5O12 over 5 days. The elemental aluminum leaching rate of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 remained low during 1-5 days of corrosion in an acidic environment. However, the singlecomponent garnet-structured aluminate ceramics exhibited a large leaching rate of ele- In addition, the (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 was designed using a pressureless sintering method, with a coefficient of thermal expansion of 9.28 × 10 −6 K −1 at 673-1273 K, approximately 18.52% higher than that of Yb 3 Al 5 O 12 (7.83 × 10 −6 K −1 , 673-1273 K), and approximately 8.67% higher than that of (Y 0.2 Yb 0.2 Lu 0.2 Eu 0.2 Er 0.2 ) 3 Al 5 O 12 (8.54 × 10 −6 K −1 , 673-1273 K); thus, this material can be applied to various substrates, such as typical hightemperature nickel-based alloys [40].
A low grain growth rate is very important for TBC materials, as it improves the crack resistance due to thermal stress and prevents an increase in thermal conductivity. Figure 8 shows the average grain sizes of the (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 ceramic specimens after annealing at 1550 • C for 7 days. As seen in Figure 8   Thermal barrier materials must have excellent chemical inertness. Figure 9 shows the normalized elemental leaching rates of Al in (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 and Yb3Al5O12 over 5 days. The elemental aluminum leaching rate of the (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 remained low during 1-5 days of corrosion in an acidic environment. However, the singlecomponent garnet-structured aluminate ceramics exhibited a large leaching rate of elemental aluminum. This result indicated that (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 ceramics have better chemical stability than Yb3Al5O12. Therefore, high-entropy aluminate ceramics are promising materials for TBCs.
The mechanical property of a TBC is also important as mechanical damage such as impact or wear can apply to the TBC. The mechanical property data of (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 are also listed in Figure 10 as a comparison. As can be seen in Figure 10, the hardness of (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 is significantly higher than that of Yb3Al5O12. The hardness of (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 is determined to be 13.3 GPa, Thermal barrier materials must have excellent chemical inertness. Figure 9 shows the normalized elemental leaching rates of Al in (Y 0. 2  which is higher than that of Yb3Al5O12 (10.7 GPa), and slightly lower than YSZ (14.0 GPa). The excellent mechanical property data suggest that (Y0.2Dy0.2Ho0.2Er0.2Yb0.2)3Al5O12 can be used as a potential thermal insulation material.  The mechanical property of a TBC is also important as mechanical damage such as impact or wear can apply to the TBC. The mechanical property data of (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 are also listed in Figure 10 as a comparison. As can be seen in Figure 10, the hardness of (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 is significantly higher than that of Yb 3 Al 5 O 12 . The hardness of (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 is determined to be 13.3 GPa, which is higher than that of Yb 3 Al 5 O 12 (10.7 GPa), and slightly lower than YSZ (14.0 GPa). The excellent mechanical property data suggest that (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 can be used as a potential thermal insulation material.

Conclusions
In summary, high-entropy rare-earth aluminate thermal barrier materials with garnet structures, (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 ceramics, were prepared by a solid-state reaction method. The results of XRD, SEM, and TEM analysis show that the synthesized (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 ceramic powder consists of a pure phase with a homogeneous rare-earth element distribution, and the lattice dimensions are a = b = c = 11.992 Å. According to the refined dimensions of the cell, the theoretical density of the (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 was calculated to be 6.02 g/cm 3 . The sintered density calculated by Archimedes' approach is 5.88 g/cm 3 , which is 97.67% of the theoretical value. The thermal conductivity of (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 ceramics is 3.48 W/(m·K) at 300 K, approximately 25.48% and 8.66% lower than that of Yb 3 Al 5 O 12 (4.67 W/(m·K)) and (Y 0.2 Yb 0.2 Lu 0.2 Eu 0.2 Er 0.2 ) 3 Al 5 O 12 (3.81 W/(m·K)). The thermal expansion of (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 is (9.28 × 10 −6 K −1 , 673-1273 K)), approximately 18.52% higher than that of Yb3Al5O12 (7.83 × 10 −6 K −1 , 673-1273 K) and approximately 8.67% higher than that of (Y 0.2 Yb 0.2 Lu 0.2 Eu 0.2 Er 0.2 ) 3 Al 5 O 12 (8.54 × 10 −6 K −1 , 673-1273 K). After annealing the (Y 0.2 Dy 0.2 Ho 0.2 Er 0.2 Yb 0.2 ) 3 Al 5 O 12 at 1550 • C, its average grain size was found to be lower than that of Yb 3 Al 5 O 12 and Er 3 Al 5 O 12 , due to the sluggish diffusion effects. As the annealing time was extended to 7 days, the average grain size of the highentropy aluminate became much smaller than that of the Yb 3 Al 5 O 12